To make the dough, heat the milk and eggnog just until it feels warm (about 100 degrees)
Sprinkle the yeast on top and leave it to sit for 10 minutes.
Whisk in the egg, butter and vanilla.
In a separate bowl, use a stand mixer, with a whisk attachment, to mix the flour and sugar. Run on low for 3 minutes.
Switch to the dough hook attachment then add the wet ingredient mixture in the center and mix on low speed until the dough comes together.
Increase to medium and knead until the dough sticks to the hook (6-8 minutes). Then shape the dough into a ball.
Clean mixer bowl and lightly grease with butter.
Return the dough to the bowl and turn to coat. Cover with a towel and allow to rise until doubled (about 1 1/2 hours).
Flour your work surface, and roll the dough into roughly 12x15" rectangle.
With the longer side facing you, spread softened butter (for the filling) over the the surface, except for 1/2" of the edge opposite you.
Mix together your sugar and cinnamon and sprinkle mixture evenly over buttered area.
Roll the dough towards the un-buttered edge, trying not to leave gaps.
Gently rub a small amount of water along the un-buttered edge and continue rolling to seal up the roll. Then cut it into 12 even pieces.
Line a 9x13" pan with parchment paper and place the cinnamon rolls in the pan, leaving a little space between each. You can use multiple smaller pans if desired. Cover with a towel and allow to rise for about 45 minutes.
Preheat the oven to 325 degrees Fahrenheit and bake until golden brown (20-30 minutes).
Cool for 15 minutes.
To make the glaze, combine powdered sugar, melted butter and eggnog and whisk until well blended.
Transfer the glaze to piping bag and drizzle over rolls.